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Nucleon Tomography--Parton Imaging in 3D
Feng Yuan Lawrence Berkeley National Laboratory
Landscape of Atomic Matter
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1( )
4a
q a sL i m F F g A
Rutherford Scattering, 1911•Discovery of nucleus
DIS at SLAC, 1960s•Discovery of quarks
Quantum ChromoDynamics:
EIC Proposals in US
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arXiv: 1108.1713, arXiv: 1212.1701
Feynman Parton: one-dimension
Inclusive cross sections probe the momentum (longitudinal) distributions of partons inside nucleon
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Hadronic reactions
DIS
Extension to transverse direction…
Semi-inclusive measurements (in DIS or Drell-Yan processes)Transverse momentum dependent
(TMD) parton distributions Deeply Virtual Compton Scattering
and Exclusive processesGeneralized parton distributions (GPD)
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Nucleon tomography
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EIC Focus
Parton’s orbital motion through the Wigner Distributions
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Phase space distribution: Projection onto p (x) to get the momentum (probability) density
Quark orbital angular momentum
Well defined in QCD:Ji, Xiong, Yuan, PRL, 2012; PRD, 2013Lorce, Pasquini, Xiong, Yuan, PRD, 2012
Outline 3D Imaging from the GPDs and TMDs
measurementsTry to answer more detailed questions as
Rutherford was doing 100 years ago QCD dynamics involved in these
processes In particular for the TMD part: universality,
factorization, evolutions,… TMDs at small-x
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TMD Parton Distributions The definition contains explicitly
the gauge links
QCD factorization has been proved for the hard processes in terms of TMDs
Collins-Soper 1981, Ji-Ma-Yuan 2004, Collins 2011
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Collins-Soper 1981, Collins 2002,Belitsky-Ji-Yuan 2002
Generalized Parton Distributions
Off-diagonal matrix elements of the quark operator (along light-cone)
It depends on quark momentum fraction x and skewness ξ, and nucleon momentum transfer t
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Mueller, et al. 1994; Ji, 1996, Radyushkin 1996
Transverse profile for the quark distribution: kt vs bt
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GPD fit to the DVCS data from HERA,Kumerick-D.Mueller, 09,10
Quark distribution calculated from a saturation-inspired modelA.Mueller 99, McLerran-Venugopalan 99
Deformation when nucleon is transversely polarized
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Lattice Calculation of the IP density ofUp quark, QCDSF/UKQCD Coll., 2006
Quark Sivers function fit to the SIDISData, Anselmino, et al. 20009
k y
kx
-0.5
0.5
0.0
-0.5 0.0 0.5
DVCS kinematics
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Experiments measure the Compton Form Factors (CFF)
Extract the GPDs The theoretical framework has been
well establishedPerturbative QCD corrections at NLO,
some at NNLO However, GPDs depend on x,ξ,t, it is
much more difficult than PDFs (only depends on x)There will be model dependence at the
beginning
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HERA HERMES
CLAS
Jlab-Hall-A
Future
HERA (ep collider) is limited by the statistics, and is not polarized
Existing fixed target experiments are limited by statistics and kinematics
Jlab 12 is limited by kinematics, in particular, Q2
Ultimate machine will be the EIC
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Transverse momentum dependent parton distribution
Straightforward extension Spin average,
helicity, and transversity distributions
PT-spin correlations Nontrivial
distributions, STXPT In quark model,
depends on S- and P-wave interference
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Sivers Asymmetries in DIS and Drell-Yan
Initial state vs. final state interactions
“Universality”: QCD prediction
HERMES/COMPASS
* *
Drell-Yan DIS
TMD predictions rely on
Non-perturbative TMDs constrained from experiments
QCD evolutions, in particular, respect to the hard momentum scale QStrong theory/phenomenological efforts in the
last few yearsNeed more exp. data/lattice calculations
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Constraints from SIDIS with Evolution
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Sun, Yuan, PRD 2013
Predictions at RHIC
Additional theory uncertainties: x-dependence of the TMDs comes from a fit to fixed target drell-yan and w/z production at Tevatron
---Nadolsky et al.
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√S = 500GeV
Drell-Yan Q=6GeV
Sun, Yuan, PRD 2013
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√S = 510GeV
-0.06-0.06
Rapidity of W Rapidity of W
Pt(GeV)Pt(GeV)
y=0y=0
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QCD evolution reduces the asymmetries abouta factor of 3 for W/Z
TMDs at small-x
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CSS
PJ>>KT
KT
Hard processes probe the kt-dependent gluon distributions directly
Saturation phenomena manifest in the observables Marquet, 2007 Dominguiz-Marquet-
Xiao-Yuan, 2010
Non-linear term at high density Balitsky-Fadin-Lipatov-Kuraev, 1977-
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Balitsky-Kovchegov: Non-linear term, 98
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Therefore
x-dependence of the TMDs at small-x, in principle, can be calculated from the QCD evolution (BK-JIMWLK)
How about Q2
It has been shown that the Sudakov double log resummation (which controls Q-evolution) can be performed consistently in the small-x formalism
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Mueller, Xiao, Yuan, PRL110,082301 (2013);Phys.Rev. D88 (2013) 114010
Two-particle correlations in central d+Au collisions at RHIC
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Stasto,Xiao,Yuan,PLB716,430(2012)
STAR and PHENIX:Broadening and Suppression two-hadron production in the back-to-back region in central d+Au collisions
Theory:QCD factorization together with gluon saturation in nucleus describes well the experimental data
PHENIX
Mapping the phase structure
RHIC
pA at LHC
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CSS
1GeV
x~10
-3
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Constantin Loizides
Mapping the phase structure
RHIC
Forward pA at LHCb and RHIC
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CSS
1GeV
x~10
-3
Computational access
Lattice calculations of the parton distributions (as functions of x) become possible by a recent proposal
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Ji, PRL110 (2013) 262002
TMDs on lattice
Nontrivial soft factor subtraction is essential to achieve the factorizationAll unwanted divergences cancelled out
Calculable on latticeshall be extended to small-x
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TMD factorization in quasi-pdfs
For example, for Drell-Yan lepton pair production
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Lattice calculationQuasi-pdfs
Soft factor
Summary There have been great progresses in
our understanding of the nucleon tomography in terms of GPDs and TMDsMore expected in the future!!!
First principle computation (lattice QCD) of nucleon tomography become possible in the future to confront the experimental data from Jlab 12 GeV upgrade and the planned EIC
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